I can't find what I'm looking for.
Maybe its just me... I actually think there's a good demand for a simple, quick PvP game, with sound logic.
I might actually make one.

You should because there is indeed a high demand for a PvP game. Im not sure why there are only a few, maybe because you can use bots for some of them to cheat but some games are pretty much not possible to cheat with bots.
Like a race cars game, there is no way to cheat that with a bot, only strategy games. So if you are going to make one make sure its not possible to cheat it.
Many action games are as easy to cheat with a bot as strategy games. And not all strategy games are easy for bots to win. If the game has too many options available, players still do better than computers.